Tag Archives: natural move monte carlo

Augmented Modelling with Natural Move Monte Carlo Simulations

In the last group meeting I reported on the progress that I have made regarding the development of a protocol for the systematic use of Natural Move Monte Carlo simulations.

Natural Move Monte Carlo simulations
Natural Moves are degrees of freedom that describe the collective motion of groups of residues. In DNA this might be the concerted motion of a double helix; in proteins this could be the movement of a stable secondary structure element such as a beta-sheet. These segments are joined by so called melting areas. At each simulation step the segments are propagated independently in an MC fashion. The resulting chain breaks are resolved by a chain closure algorithm that acts on the melting areas. This results in a reduction of degrees of freedom of several orders of magnitude. Therefore, large complexes and conformational changes can be sampled more effectively.

In order to get sensible results, however, the initial decomposition of the system is important. The challenge is to accurately represent the plasticity of the system, while keeping the number of degrees of freedom as small as possible. Detailed insight into the flexibility of the system might be gained from experimental sources such as NMR or computational methods such as MD simulations and Normal Mode Analysis. This can help with defining segments and melting areas. However, there are many systems for which this data is not available. Even if it is, there is no guarantee that the segmentation is correct.

Therefore, I am developing a protocol that allows for the evaluation of a range of different test cases that each reflect a unique set of segments and melting areas.

Augmented Modelling Protocol
This protocol is aimed at the systematic evaluation of NMMC segmentations. It allows researchers to feed experimental information, biological knowledge and educated guesses into molecular simulations and so provides a framework for testing competing hypotheses. The protocol has four steps.

Step 1: Segmentation of the system into low-level segments
The initial segmentation contains all possible areas of flexibility that may play a role in conformational changes in the system of interest. This decision may be influenced by many sources. For now, however, we only consider secondary structure information. Helices and beta strands are treated as potential segments. Unstructured regions such as kinks, loops and random coils are treated as melting areas. For a small fold with four helices we get the segmentation shown in figure 1a.

Step 2: Formulate test cases
Generate multiple test cases that reflect hypotheses about the mechanism of interest. In this step we try to narrow down the degrees of freedom as much as possible in order to retain sampling efficiency. This is done by selectively deactivating some melting areas that were defined in step 1. For a system with three melting areas that can either be on or off, 2^3 = 8 different test cases may be generated (example shown in figure 1b).

Segmentation of a small α-fold.

Figure 1 a) Segmentation of a small α-fold. The blue rectangles represent α-helices. The dashed lines indicate the presence of melting areas I, II and III. Each melting area can be switched on or off (1/0) b) Example of a test case in which the first of three melting area is switched off. c) The six degrees of freedom along which a segment is propagated.

Step 3: Perform simulations
Sample the conformational space of all test cases that were generated in step 2. We generally use Parallel Tempering or Simulated Tempering algorithm to accelerate the sampling process. These methods rely on the modulation of temperature to overcome energy barriers.

Step 4: Evaluate results
Score the results against a given control and rank the test cases accordingly. The scoring might be done by comparing experimental distributions of observables with those generated by simulations (e.g. Kullback-Leibler divergence). A test case that reproduces desired expectation values of observables might then be considered as a candidate hypothesis for a certain structural mechanism.

What’s next?
I am currently working on example uses for this protocol. These include questions regarding aspects of protein folding and the stability of the empty MHC II binding groove.

Natural Move Monte Carlo: Sampling Collective Motions in Proteins

Protein and RNA structures are built up in a hierarchical fashion: from linear chains and random coils (primary) to local substructures (secondary) that make up a subunit’s 3D geometry (tertiary) which in turn can interact with additional subunits to form homomeric or heteromeric multimers (quaternary). The metastable nature of the folded polymer enables it to carry out its function repeatedly while avoiding aggregation and degradation. These functions often rely on structural motions that involve multiple scales of conformational changes by moving residues, secondary structure elements, protein domains or even whole subunits collectively around a small set of degrees of freedom.

The modular architecture of antibodies, makes them amenable to act as an example for this phenomenon. Using MD simulations and fluorescence anisotropy experiments Kortkhonjia et al. observed that Ig domain motions in their antibody of interest were shown to correlate on two levels: 1) with laterally neighbouring Ig domains (i.e. VH with VL and CH1 with CL) and 2) with their respective Fab and Fc regions.

Correlated Motion

Correlated motion between all residue pairs of an antibody during an MD simulation. The axes identify the residues whereas the colours light up as the correlation in motion increases. The individual Ig domains as well as the two Fabs and the Fc can be easily identified. ref: Kortkhonjia, et al., MAbs. Vol. 5. No. 2. Landes Bioscience, 2013.

This begs the question: Can we exploit these molecular properties to reduce dimensionality and overcome energy barriers when sampling the functional motions of metastable proteins?

In 2012 Sim et al. have published an approach that allows for the incorporation of these collective motions (they call them “Natural Moves”) into simulation. Using simple RNA model structures they have shown that explicitly sampling large structural moves can significantly accelerate the sampling process in their Monte Carlo simulation. By gradually introducing DOFs that propagate increasingly large substructures of the molecule they managed to reduce the convergence time by several orders of magnitude. This can be ascribed to the resulting reduction of the search space that narrows down the sampling window. Instead of sampling all possible conformations that a given polynucleotide chain may take, structural states that differ from the native state predominantly in tertiary structure are explored.

Reduced Dimensionality

Reducing the conformational search space by introducing Natural Moves. A) Ω1 (residue-level flexibility) represents the cube, Ω2 (collective motions of helices) spans the plane and Ω3 (collective motions of Ω2 bodies) is shown as a line. B) By integrating multiple layers of Natural Moves the dimensionality is reduced. ref: Sim et al. (2012). PNAS 109(8), 2890–5. doi:10.1073/pnas.1119918109

It is important to stress, however, that in addition to these rigid body moves local flexibility is maintained by preserving residue level flexibility. Consequently, the authors argue, high energy barriers resulting from large structural rearrangements are reduced and the resulting energy landscape is smoothened. Therefore, entrapment in local energy minima becomes less likely and the acceptance rate of the Monte Carlo simulation is improved.

Although benchmarking of this method has mostly relied on case studies involving model RNA structures with near perfect symmetry, this method has a natural link to near-native protein structure sampling. Similarly to RNA, proteins can be decomposed into local substructures that may be responsible for the main functional motions in a given protein. However, due to the complexity of protein motion and limited experimental data we have a limited understanding of protein dynamics. This makes it a challenging task to identify suitable decompositions. As more dynamic data emerges from biophysical methods such as NMR spectroscopy and databases such as www.dynameomics.org are extended we will be able to better approximate protein motions with Natural Moves.

In conclusion, when applied to suitable systems and when used with care, there is an opportunity to breathe life into the static macromolecules of the pdb, which may help to improve our understanding of the heterogeneous structural landscape and the functional motions of metastable proteins and nanomachines.